The Economic Writings of Sir William Petty/Volume 1/Introduction/GrauntStat

by William Petty

 

GRAUNT AND THE SCIENCE OF STATISTICS.

As statistical writing Graunt's "Observations upon the Bills of Mortality" are superior to any of Petty's works. Indeed they alone can claim to be "statistics"; Petty's "Essays" are so different in character that his own name of "political arithmetick" is still their most accurate description. The difference, as has been pointed out^[1], arises in part rather from Graunt's sparing use of calculation than from any especial merit in such calculations as he does make. His estimate of London's population^[2] is superior to Petty's in no way unless it be by reason of priority; and his table of mortality is as pure guess work as anything that Petty ever wrote^[3]. But the difference between them cannot be wholly explained by the circumstance that Graunt's temptation to reckon was less than Petty's because his data were more complete. The spirit of their work is often different when no question of calculation enters. Petty sometimes appears to be seeking figures that will support a conclusion which he has already reached: Graunt uses his numerical data as a basis for conclusions, declining to go beyond them^[4]. He is thus a more careful statistician than Petty, but he is not an economist at all.

Some of the most important facts which the study of vital statistics has yet discovered were first brought to light by Graunt. Though they may be read at length in his "Observations" here reprinted, it is essential to an adequate appreciation of his merits that the more pregnant of his discoveries be brought together by way of summary. Four are particularly noteworthy. In the first place, the regularity of certain social phenomena which appear to be, in their individual occurrence, the sport of chance, was first made evident by Graunt's studies. One of his earliest observations is, "That among the several Casualties some bear a constant proportion unto the whole number of Burials; such are Chronical Diseases, and the Diseases whereunto the City is most subject; as for Example, Consumptions, Dropsies, Jaundice, Gout, Stone, Palsie, Scurvy, Rising of the Lights or Mother, Rickets, Aged, Agues, Fevers, Bloody Flux and Scowring: nay, some Accidents, as Grief, Drowning, Men's making away themselves, and being Kill'd by several Accidents, &c. do the like^[5]." From the regularity of these phenomena, however, for example of suicide, Graunt deduces no such moral implications as Quetelet and Buckle, not to mention living writers, have sought to place upon it. In the second place Graunt first noted the excess of male over female births and the approximate numerical equality of the sexes, and upon it he bases some remarks about Divine approval of monogamy^[6]. His suggestion had great vogue and is often repeated. The third among the important facts which Graunt discovered is the high rate of mortality during the earlier years of life; the fourth is the excess of the urban over the rural death rate. In establishing the first two of these four facts Graunt called attention to truths previously unrecognized. It is not improbable, on the other hand, that the facts regarding mortality had been conjectured before his time. But he was the first to verify conjecture by observations so extended that they resulted in demonstration. Proof, indeed, is the characteristic feature of his book. The fulness of his proof and the care with which he elaborates it raise his "Observations" to a higher plane than is reached by any similar investigation of social phenomena during the century that lies between Graunt and Süssmilch.

It cannot be contended that Graunt was completely master of the method of investigation to which he made noteworthy contributions. His imperfect apprehension of the so-called law of large numbers appears clearly in his discussion of the country bills. "The proportion," he says^[7] "Between the greatest and the least mortalities in the Country is far greater than at London... as in London in no Decad the burials of one year are double to those of another, so in the Country they are seldom not more than so... which shows that the opener and freer Airs are most subject to the good and bad Impressions." This is an attempt to explain by physical conditions the wide range in the observed country death rate which is really due to the narrowness of the field—a single market town—under investigation. It is, perhaps, the gravest statistical mistake that can be charged against Graunt. And when we remember that he was a statistical pioneer, blazing his way through a trackless forest, we must confess surprise that his faults are so few and his merits so many. He had not enjoyed the academic training of most of his associates in the Royal Society, but he was permeated with the spirit of that new philosophy which bade curiosity turn for satisfaction rather to observation than to speculation. His book, with all its faults, deserves a place among the penetrating and fearless treatises which, marred though they were by much now known to be absurd, still contributed to render even the early years of the Royal Society illustrious.

Graunt's influence upon later statistical writers can be traced with remarkable distinctness. Petty is the first to acknowledge as he was the first to feel it; but his obligation is of that vital sort which no series of quotations can sufficiently express. How largely his best work depends upon Graunt can be appreciated only by reading in connection with Graunt's "Observations" the second volume of Petty's Economic Writings. Upon Halley's "Estimate of the Degrees of Mortality of Mankind" (1693) Graunt's influence is not quite so obvious. But anyone who has read, as to some extent I have, the scattered letters of Petty, Southwell, Williamson, Pett, and Justel, all members of the Royal Society and friends of Petty, and all but Justel acquainted with Graunt, cannot fail to see how, as a result of Graunt's and Petty's efforts, the air surrounding Halley was full of political arithmetic. He turned his great abilities as it were casually and but for a few days to that subject; but he seized at once upon Graunt's most striking discovery, the regularity of death, and utilized it for the first suggestion of life insurance. Of Gregory King and Charles Davenant it is not necessary to speak. They belong rather to Petty's school than to Graunt's. The next link in the chain of Graunt's influence is the Rev. William Derham (1657-1735). As Boyle lecturer in 1711-12 Derham, having the honour to be a member of the Royal Society as well as a divine, was minded to try what he could do toward the improvement of philosophical matters to theological uses. While writing his lectures^[8] with this in view, he happened upon Graunt's book, which caused him to see that the constant proportion of marriages to births and of births to burials constitutes "a wise means to keep the balance of mankind even;" and he concludes his discussion by asking "upon the whole matter, what is all this but admirable plan and management? What can the maintaining, throughout all ages and places, of these proportions of mankind, and all other creatures; this harmony in the generations of man be but the work of One that ruleth the world?^[9]" Of themselves Derham's remarks, which are but incidental to a comprehensive argument from design, would be of small significance in the history of statistics. But they chanced, because they were in a theological book, to fall into the hands of a Prussian tutor and military chaplain, who made them matter for investigation.

Johann Peter Süssmilch (1707-1767) was not, as Roscher asserts^[10], the first to make the growth of population a subject of independent investigation on its own account^[11]: Graunt certainly anticipated him in that. But he was perhaps the first who clearly grasped the fact, which escaped Graunt, that when and only when sufficiently large numbers are taken into account, order and not accident appear. It is not my intention to describe Süssmilch's book, the great ability of which is now everywhere recognized. But since many of his countrymen have represented him as the founder of statistics in the modern sense, or of vital statistics, it is worth while to point out that Süssmilch himself considers Graunt his master. "Die göttliche Ordnung" was first suggested, he tells us, by the observations collected by Derham^[12]. Becoming interested in the subject, he sent to England for the writings of Graunt and Petty^[13], and was thus induced to publish his book partly because the observations already made were known to very few people, partly because the lists which he had collected in Germany enabled him to go further in some respects than Graunt and Petty had done^[14]. But to Graunt, as he acknowledges^[15], the first and most distinguished praise belongs. Graunt first sought to utilize the bills for the discovery of the new truths. Parish registers had been kept for centuries, but who before Graunt used them to lay bare "Die göttliche Ordnung?" The discovery was as possible as that of America, all that was wanting was a Columbus who should go further than others in his survey of old and well known truths and reports. That Columbus was Graunt^[16].

The influence of Süssmilch upon Malthus has never been traced. The first suggestion of the "Essay on the Principle of Population" owes nothing to "Die göttliche Ordnung," but in every edition after the first Süssmilch is cited between forty and fifty times. It was doubtless to one of the later editions that the author of "The Origin of Species" acknowledges his indebtedness for what is perhaps the central idea of his work.

"The Observations upon the London Bills of Mortality," wrote Petty at the outset of the statistical work which first engaged his own attention^[17], "have been a new Light to the World; and the like Observation upon those of Dublin may serve as Snuffers to make the same candle burn clearer." It is improbable that even Petty, in spite of the openness of his mind and the vigour of his imagination, appreciated to the full the significance of Graunt's discoveries; but it may perhaps be noted that he wrote of another great work of his day, "Poor Mr Newton... I have not met with one man that putt an extraordinary value on his book. I would give 500l. to have been the author of it; and 200l. that Charles understood it^[18]."

---

1. P. lxvi.
2. Pp. 384—386.
3. On p. 387. I have there suggested a reason for suspecting that Petty may have concocted the table.
4. Cf. pp. 355 § 12, 357 § 21.
5. P. 352. "Die Lehre von der sogenannten Gesetzmassigkeit der scheinbar freiwilligen Handlungen ist schon von Condorcet [!] ausgesprochen." Meitzen, Geschichte, Theorie und Tecknik der Statistik, 118.
6. Pp- 374—378.
7. Pp. 391—392.
8. Physico-theology; or a Demonstration of the Being and Attributes of God from his Works of Creation. 1713. I cite the "new edition" of 1798.
9. Ibid., i., 267.
10. Geschichte der Nationalökonomik in Deutschland, 421.
11. The title of Süssmilch's book shows plainly that, like Derham, he was interested primarily in the theological implications of vital statistics. It runs: Die göttliche Ordnung in den Veranderungen des menschlichen Geschlechts aus der Geburt, dem Tode und der Fortpflanzung desselben erwiesen...worin die Regeln der Ordnung bewiesen werden, welche Gottes Weisheit und Güte in dem Lauf der Natur zur Erhaltung, Vermehrung und Verdopplung des menschlichen Geschlechts festgesetzt hat,... Berlin, J. C. Spener, 1741. I cite the pirated ed. published at Berlin by Gahls in 1742. See W. F. Willcox and F. S. Crum, A trial bibliography of the writings of Süssmilch., Publ, Amer. Statistical Assn, V. 310—314.
12. Süssmilch, 13.
13. Ibid., 16.
14. Ibid., 27.
15. Ibid., 17.
16. Ibid., 18.
17. P. 398, note.
18. To Southwell, 9 July, 1687, Fitzmaurice, 306, 307. Charles was Petty's eldest son.